In this section, we discuss, somewhat informally, the obstacles that arise in transferring
to trace languages the results and methods from the algebraic theory of word languages,
focusing on results which rely on the wreath product operation: the wreath product
principle (see [1]}) and the Krohn-Rhodes theorem (see
[2]}).
We first recall the definitions of division, simulation and wreath products in the context
of transformation monoids, see [2]}.
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